| Euclides - 1845
...EFGH above the space S; because, by the preceding Lemma, if from the greater of two unequal magnitudes **there be taken more than its half, and from the remainder...there shall at length remain a magnitude less than** the least of the proposed magnitudes. Let then the segments EK, KF, FL, LG, GM, MH, HN, NE be those... | |
| Scottish school-book assoc - 1845
...given line. For it has been shown in the proposition that this is equivalent to taking away from EC **more than its half, and from the remainder more than its half, and so on** continually ; .-. (Prop. 73, Cor.) the quantity ultimately left is less than any given quantity. PROPOSITION... | |
| Euclides - 1846
...less than any other given magnitude less than the former. Let AB and C be the two given magnitudes, **of which AB is the greater : if from AB there be taken** a magnitude greater than its half, and from the remainder a magnitude greater than its half, and so... | |
| John Playfair - 1846 - 317 sider
...a magnitude less than the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, **of which AB is the greater. If from AB there be taken** away its half, and from the remainder its half, and so on ; there shall at length remain a magnitude... | |
| Euclides - 1848
...equal to one another. BOOK XII. PROPOSITIONS. LEMMA I. IP from the greater of two unequal magnitudes, **there be taken more than its half, and from the remainder...there shall at length remain a magnitude less than** the least of the proposed magnitudes. (Book x. Prop, i.) PROP. I. THEOREM. Similar polygons inscribed... | |
| Euclides - 1855
...of the proposed magnitudes. Let AB and C be two unequal magnitudes, of the same kind, of which \ B **is the greater. If from AB there be taken more than...the remainder more than its half, and so on ; there** will at length remain a magnitude less than C. For C may be multiplied so as at length to become greater... | |
| Euclides - 1855
...hexagon. T. Of the Multiples of Magnitudes. HYPOTHESES. If from the greater of two unequal magnitudes, **there be taken more than its half, and from the remainder more than its half, and so on.** If one magnitude be the same multiple of another, which a part taken from the first is of a part taken... | |
| Eucleides - 1860
...160). V. 6. . . V. 1. . . V. c. (p. 34). HYPOTHESES. If from the greater of two unequal magnitudes, **there be taken more than its half, and from the remainder more than its half, and so on.** If one magnitude be the same multiple of another, which a part taken from the first is of a part taken... | |
| Euclides - 1860
...a magnitude less than the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, **of which AB is the greater. If from AB there be taken** away its half, and from the remainder its half, and so on, there shall at length remain a magnitude... | |
| Euclides - 1864
...EFGH above the space 8; because, by the preceding Lemma, if from the greater of two unequal magnitudes **there be taken more than its half, and from the remainder...there shall at length remain a magnitude less than** the least of the proposed magnitudes. Let then the segments EK, KF, FL, LG, GM, MH, HN, NE be those... | |
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